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Vortex generation by deep-water breaking waves

Published online by Cambridge University Press:  08 October 2013

N. E. Pizzo  and
W. Kendall Melville
N. E. Pizzo*
Affiliation:
Scripps Institution of Oceanography, University of California, San Diego, La Jolla, CA 92093-0213, USA
W. Kendall Melville
Affiliation:
Scripps Institution of Oceanography, University of California, San Diego, La Jolla, CA 92093-0213, USA
*
†Email address for correspondence: npizzo@ucsd.edu
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Abstract

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The connection between wave dissipation by breaking deep-water surface gravity waves and the resulting turbulence and mixing is crucial for an improved understanding of air–sea interaction processes. Starting with the ensemble-averaged Euler equations, governing the evolution of the mean flow, we model the forcing, associated with the breaking-induced Reynolds shear stresses, as a body force describing the bulk scale effects of a breaking deep-water surface gravity wave on the water column. From this, we derive an equation describing the generation of circulation, $\Gamma $, of the ensemble-average velocity field, due to the body force. By examining the relationship between a breaking wave and an impulsively forced fluid, we propose a functional form for the body force, allowing us to build upon the classical work on vortex ring phenomena to both quantify the circulation generated by a breaking wave and describe the vortex structure of the induced motion. Using scaling arguments, we show that $\Gamma = \alpha {(hk)}^{3/ 2} {c}^{3} / g$, where ($c, h, k$) represent a characteristic speed, height and wavenumber of the breaking wave, respectively, $g$ is the acceleration due to gravity and $\alpha $ is a constant. This then allows us to find a direct relationship between the circulation and the wave energy dissipation rate per unit crest length due to breaking, ${\epsilon }_{l} $. Finally, we compare our model and the available experimental data.

JFM classification

Geophysical and Geological Flows: Air/sea interactions Vortex Flows: Vortex Flows Waves/Free-surface Flows: Wave breaking
Type
Papers
Information
Journal of Fluid Mechanics , Volume 734 , 10 November 2013 , pp. 198 - 218
Creative Commons
Creative Common License - CCCreative Common License - BY
The online version of this article is published within an Open Access environment subject to the conditions of the Creative Commons Attribution licence .
Copyright
©2013 Cambridge University Press.

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